A349286 G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(3*x)^2).

1, 1, 7, 148, 8695, 1455433, 715092412, 1046279830240, 4581706851060703, 60144130721142806611, 2367934845363738749478583, 279660212608573899258160179472, 99083333806943049370375436233999876, 105314387436569180750449877597844106742044

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 3^(i+j) * a(i) * a(j) * a(n-i-j-1).

a(n) ~ c * 3^(n*(n-1)/2) * 2^n, where c = 0.7827821536020754599551185976017878354967268590673601224489106938395... - Vaclav Kotesovec, Nov 13 2021

Mathematica

nmax = 13; A[_] = 0; Do[A[x_] = 1/(1 - x A[3 x]^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[3^(i + j) a[i] a[j] a[n - i - j - 1], {j, 0, n - i - 1}], {i, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Crossrefs

Cf. A001764, A015084, A171192, A349287.

Sequence in context: A048935 A291677 A152552 * A308581 A305467 A229806

Adjacent sequences: A349283 A349284 A349285 * A349287 A349288 A349289

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2021

Status

approved